Nick Brown Smelled Bull

A plucky amateur dared to question a celebrated psychological finding. He wound up blowing the whole theory wide open.

Illustrations by Kevin Huizenga

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It was autumn of 2011. Sitting in a dimly lit London classroom, taking notes from a teacher’s slides, Nick Brown could not believe his eyes.

By training a computers man, the then-fifty-year-old Brit was looking to beef up his people skills, and had enrolled in a part-time course in applied positive psychology at the University of East London. "Evidence-based stuff" is how the field of “positive human functioning” had been explained to him—scientific and rigorous.

So then what was this? A butterfly graph, the calling card of chaos theory mathematics, purporting to show the tipping point upon which individuals and groups “flourish” or “languish.” Not a metaphor, no poetic allusion, but an exact ratio: 2.9013 positive to 1 negative emotions. Cultivate a “positivity ratio” of greater than 2.9-to-1 and sail smoothly through life; fall below it, and sink like a stone.

The theory was well credentialed. Now cited in academic journals over 350 times, it was first put forth in a 2005 paper by Barbara Fredrickson, a luminary of the positive psychology movement, and Marcial Losada, a Chilean management consultant, and published in the American Psychologist, the flagship peer-reviewed journal of the largest organization of psychologists in the U.S.

But Brown smelled bullshit. A universal constant predicting success and fulfillment, failure and discontent? "In what world could this be true?" he wondered.

When class was over, he tapped the shoulder of a schoolmate he knew had a background in natural sciences, but the man only shrugged.

“I just got a bee in my bonnet,” Brown says.

* * *

Before enrolling in the positive psychology program at the University of East London, Brown had been in a self-described “rut.”

The married father of two had graduated from Cambridge University in 1981 with a degree in computer science, and spent most of his career as an IT networks operator at an international organization in Strasbourg, France.

After nearly twenty years in the position, stretched thin between technical duties and managerial headaches, he was looking for something new. So he jumped at the chance to transfer into human resources when it presented itself. The move didn’t deliver the change he was expecting, however. Still operating in a large bureaucracy—the same organization, in fact—Brown was now tasked with promoting staff welfare. But he had “little leeway to make decisions,” and was constantly signing off on stuff he "thought was just plain wrong.” Adding insult to injury, when charged with renewing his company’s suppliers list for training and coaching materials, he wound up interacting with “nuts” and “charlatans,” people who listed reiki and crystal healing among their interests, or resorted to “hand-waving” when selling their wares.

He was fed up. Coming up on fifty, his mother ailing, “the general BS, the constant, not particularly high, but nonstop level of moderate dishonesty,” was beginning to wear on him.

Then one day in November 2010, Brown happened to find himself at a Manchester conference attending a talk by popular British psychologist Richard Wiseman, who had written a book called The Luck Factor.

"Basically, the way to be lucky is to just put yourself in situations where good things can happen," Brown remembers, "because more good things will happen to you than bad on any given day, but nothing will happen to you if you just sit indoors.”

After the talk, Wiseman signed books. The pile dwindled down and down, and only four books remained when Brown made it near the front of the line. Four people were standing between him and Wiseman.

"I thought, 'Well okay I’m not going to get one,'" he says. "And then I was about two feet from the front, and the woman in front of me, she was one step away from him—had been queuing for twenty minutes—she just decided she didn’t want a book anymore and walked off.”

The two men laughed and got to talking. Brown explained his situation at work. He asked Wiseman where he could find “evidenced-based stuff,” science-backed skills he could use to motivate employees and gain the upper hand of the hucksters and quacks hawking Tony Robbins-esque fluff.

The emerging field, Wiseman said, was called positive psychology.

* * *

As described by the Oxford University Press, positive psychology aims “to study positive human nature, using only the most rigorous scientific tools and theories.”

In a 1998 president’s address, then-president of the American Psychological Association Martin Seligman announced the birth of positive psychology, calling it, “a reoriented science that emphasizes the understanding and building of the most positive qualities of an individual: optimism, courage, work ethic, future-mindedness, interpersonal skill, the capacity for pleasure and insight, and social responsibility.”

In large part, positive psychology can be defined by what it is not—the study of mental illness (rather, it aims to preempt it)—and in contrast to what came before it—a branch of the social sciences called humanistic psychology that focuses on “growth-oriented” aspects of human nature, but which some in positive psychology criticize as not being adequately scientific.

A typical positive psychology exercise, as described by Seligman, the movement’s most visible figure, in his popular 2011 book Flourish, goes like so:

“Every night for the next week, set aside ten minutes before you go to sleep. Write down three things that went well today and why they went well.”

The “What Went Well” or “Three Blessings” exercise, which is known in positive psychology as a “positive intervention,” comes as part of a package of treatments collectively called positive psychotherapy. And in a study of people with severe depression, Seligman found that positive psychotherapy relieved, “depressive symptoms on all outcome measures better than treatment as usual and better than drugs.”

Similar findings have afforded positive psychology a level of public credibility that few other psychological subfields enjoy. Centers and academic programs have sprouted up across the world, the most influential of them being Seligman’s own one-year, $45,000 Master of Applied Positive Psychology program at the University of Pennsylvania.

In 2002, with a $2.8 million grant from the U.S. Department of Education, the Penn Resiliency Program (part of the University of Pennsylvania's Positive Psychology Center) began a four-year study of positive psychology’s effects on ninth-graders at a high school outside of Philadelphia. Six years later, in 2008, Seligman entered into a far-reaching collaboration with the U.S. Army, resulting in a $125 million government-funded “Army-wide” program known as Comprehensive Soldier Fitness (CSF).

Guest-editing a January 2011 special edition of the American Psychologist that was dedicated to the program, Seligman wrote, along with two military personnel, that CSF's goal is to, “increase the number of soldiers who derive meaning and personal growth from their combat experience,” and "to decrease the number of soldiers who develop stress pathologies."

Recently, however, it has been reported that CSF has done little to reduce PTSD. Nevertheless, the government is expanding the $50-million-per-year program.

One of the authors who contributed to the American Psychologist’s special edition on Comprehensive Soldier Fitness was Barbara Fredrickson. Co-writing "Emotional Fitness and the Movement of Affective Science from Lab to Field," she cited her 2005 work on the "critical positivity ratio."

Fredrickson is best known for her “broaden-and-build” theory, which posits that the cultivation of positive emotions promotes greater and greater wellbeing. She is considered a rock star of the positive psychology movement, once having been praised by Seligman as its “laboratory genius.” Over the course of her career, according to her curriculum vitae, she has received $240,000 in awards and fellowships and over $9 million in grant funding.

Where the concept of a ratio of positive to negative emotions dates back to the 1950s, the specific origin of the critical positivity ratio took place in 2003, writes Fredrickson in her general readership book Positivity: Top-Notch Research Reveals the 3-to-1 Ratio That Will Change Your Life.

A Chilean business-consultant named Marcial Losada, "who had begun to dabble in what had become his passion: mathematical modeling of group behavior," sent her an out-of-the-blue email. Appealing to research he performed in the 1990s that coded the language of sixty business teams for positive and negative affect, Losada said he had “developed a mathematical model—based on nonlinear dynamics—of (Fredrickson's) broaden-and-build theory.”

Two independent tests by Fredrickson studying the emotional ratios of individuals seemed to confirm Losada's findings. In 2005, the two unveiled the critical positive ratio in an American Psychologist paper titled “Positive Affect and the Complex Dynamics of Human Flourishing.”

The theory was bolder than bold: Mankind, whether working alone or in groups, is governed by a mathematical tipping point, one specified by a ratio of 2.9013 positive to 1 negative emotions. When the tipping point is crested, a kind of positive emotional chaos ensues—“that flapping of the butterfly’s wing,” as Fredrickson puts it—resulting in human “flourishing.” When it is not met (or if a limit of 11.6346 positive emotions is exceeded, as there is a limit to positivity), everything comes grinding to a halt, or locks into stereotyped patterns like water freezing into ice.

In Positivity, Fredrickson writes that it is possible to promote positive emotions and decrease negative ones. The critical positivity ratio, then, represented a stark dividing line—the difference between a bummer of a life and a blissful one. Feel good about twelve things in your day and bad only about four, and by the laws of the ratio you'll be happy. Knock just one of the good emotions out, however, and you won’t. So get that extra cookie and talk with someone you love, and push yourself over the mathematical hump.

Less than a month into his program at the University of East London, Nick Brown was making breakthroughs of his own.

He had been poring over the original papers that informed Fredrickson and Losada’s 2005 article—papers written or co-written by Marcial Losada. They seemed “sketchy,” Brown says. In his research on business teams, for instance, “the length of the business meetings weren’t even mentioned.”

“Normally you have a method and the method says we selected these people and we picked these numbers and here’s the tables and here are the means and here’s the standard deviation,” Brown says. “He just goes: ‘Satisfied that the model fit my data, I then ran some simulations.’ The whole process was indistinguishable from him having made the data up.”

In scrutinizing Fredrickson and Losada's work, Brown happened upon a line in their 2005 paper that caught his attention: “Losada (1999) established the equivalence between his control parameter, c, and the Lorenzian control parameter, r. Using the above equation, it is known that the positivity ratio equivalent to r = 24.7368 is 2.9013.”

“So I started looking for where that formula came from," he says.

He dug out a famed 1963 paper by the American mathematician and meteorologist Edward Lorenz on nonlinear aspects of fluid mechanics, a subdiscipline of fluid dynamics—or the study of liquids and gases in motion.

“I couldn’t read most of it,” Brown says. “It’s a proper physics paper. But I started digging into it, and I managed to find one equation that I could read, and which when I plugged in the numbers”—the constants that Lorenz chose for convenience in 1963—“came out with the positivity ratio.”

“I thought, ‘Yes, I’ve got it.’”

It seemed a case of numbers fudging. In a valid fluid dynamics problem, the numbers plugged into the equation must correlate to the properties of the fluid being studied. But in attempting to draw an equivalence between the physical flow of liquids and the emotional “flow” of human beings, Losada had simply lifted the numbers that Lorenz used in 1963 to explain his method in the abstract, numbers used merely for illustrative purposes. Losada’s results, along with the pretty butterfly graphs Brown had been shown in class, were essentially meaningless.

Brown knew he was on to something. He knew equally well he would need help dotting his mathematical I's and crossing his psychological T's.

When a teacher at University of East London suggested he contact Fredrickson directly and say he’d found a mistake, he resisted. “It occurred to me that the level of proof someone would have to bring to me if I was Dr. Fredrickson, if I was a senior professor and you were a grad student who’d been in psychology for three weeks, would have to be pretty big.”

So he went Googling instead, sending out emails to academics and researchers he suspected might be sympathetic to his cause.

On December 5th, he got a response.

* * *

Harris Friedman lives in a wilderness reserve near the Florida Everglades. A sixty-five-year-old psychology professor at the University of Florida and a Professor Emeritus at Saybrook Graduate School, he calls himself, “one of these people who likes to think deeply about issues in psychology that most take for granted and think of as givens.”

Friedman worries about "faddish things" in his field. As a disciple of the humanistic psychological tradition, he was chagrined when positive psychology erupted onto the scene in what he calls “a burst of negativity.”

In 2000, writing in the American Psychologist, Martin Seligman and fellow positive psychology pioneer Mihaly Csikszentmihalyi wrote that humanistic psychology failed to “attract much of a cumulative empirical base,” that it, “spawned myriad therapeutic self-help movements,” and that the legacy of the movement is “prominently displayed in any large bookstore,” with the “‘psychology’ section (containing) at least 10 shelves on crystal healing, aromatherapy, and reaching the inner child for every shelf of books that tries to uphold some scholarly standard.”

The dig “got a major groan out of me,” says Friedman, who prides himself on the rigor of his work and the legacy of humanism.

Psychology has long been vexed by the question of the quantitative vs. the qualitative, resulting in a kind of shame known as “physics envy,” whereby researchers in so-called “softer” social sciences feel inadequate when compared to “harder” physical sciences. Friedman says he tries to take a balanced view on the subject. Seligman, on the other hand, he says, “claims that quantitative work is more rigorous than qualitative, and that’s something I dispute. Each can be rigorous in their own way, and each can be misused.”

And misused was exactly the word on his mind when he read Fredrickson and Losada's paper upon its publication in 2005. "I recollect just letting out a sigh," he says, "just more stuff of dubious worth."

So he was intrigued when he received Brown’s email six years later, asking for help to take it down.

"Dear Dr. Friedman,

Please excuse me writing to you spontaneously like this..."

“I had no idea what his background was,” Friedman says, “I didn’t know if it was suitable, and I didn’t know how to tackle the math myself, so essentially I responded, ‘I’m willing to play, tell me what’s on your mind.’”

Friedman suggested that Brown start drafting a critique. “He began to make sense,” Friedman says. “Nick intuitively saw the flaws in the mathematics. He realized how implausible this was.”

“But he couldn’t pin it down,” he says. The math was too much.

* * *

Enter Alan Sokal. A mathematician and physicist, Sokal is best known for a trick he played over a decade ago, now known simply as the “Sokal Affair.”

In 1996, wanting to see if, “a leading North American journal of cultural studies…would publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors' ideological preconceptions,” Sokal submitted a paper to a postmodern cultural studies journal called Social Text that made little to no sense, and ended up getting it published. A great deal of controversy ensued when Sokal announced his hoax, and a year afterward he co-wrote a popular book titled Intellectual Impostures.

“I guess I’m seen as an all-purpose fighter against bullshit," says Sokal, now fifty-eight years old, with a voice reminiscent of Phil Hartman.

Brown had emailed the science gadfly in late November of 2011, but Sokal, who was swamped with papers and class work, had filed it away. He had received similar emails before, emails asking him for help debunking bad science, “several times a year,” he says, “some less serious, some more serious.”

More often than not, the emails got lost in the mix, but somehow, combing through his correspondence a few weeks later, he happened across Brown’s and started reading.

Sokal “didn’t know what positive psychology was at the time,” he says, but he saw that the issue was in his domain—“a misuse of math and physics”—and that the mathematical offense was particularly obvious. “This one wasn’t even hard.”

Brown related a list of inconsistencies he had found in the mathematical guts of the theory. Finishing his email, he wrote:

“Here's my problem. I am just this grad student with no qualifications or credentials, starting out in the field. I don't know how to express this kind of idea especially coherently in academic written form, and I suspect that even if I did, it would be unlikely to be published."

"On the other hand,” he continued, “I don't think that I'm a crank, and this is starting to bug me…I would be very happy to be proved ignorant on this, by someone who understands the science and mathematics better than I do."

Sokal responded that he was “quite impressed with the cogency” of Brown’s critique, and encouraged him to develop it into a full paper for publishing. Later, the two met up for lunch in London, where Brown was studying and Sokal was teaching. Soon after, another email reached Brown’s inbox.

Sokal, “came back with my draft one day,” Brown says, “and had written 3,000 words.”

* * *

By the late winter of 2012, Friedman, Sokal and Brown were all in touch via email and working together towards a draft of what would become “The Complex Dynamics of Wishful Thinking.”

The three men brought different skills to the plate. Brown was the outsider, the instigator, who, knowing no better, dared to question the theory in the first place. Friedman provided psychological expertise and played a diplomatic role, helping guide the paper towards publication. Sokal was the finisher, the infamous debunker with the know-how needed to dismantle the theory in hard, mathematic language.

The article they wrote not only took to pieces Fredrickson and Losada’s 2005 paper, but also two earlier articles written or co-written by Losada. Taken together, Brown, Sokal and Freidman tallied a litany of abuses, which they related, one by one, in painstaking detail.

“We shall demonstrate that each one of the three articles is completely vitiated by fundamental conceptual and mathematical errors,” they wrote.

But before getting to those fundamental errors, they agreed it would be best to begin the piece with a rudimentary explanation of differential equations, the mathematical building blocks that Losada and Fredrickson misused, and how they work.

The pedagogical intro was written by Sokal and intended to have a two-pronged effect. On the one hand, it enabled “anybody with one undergrad course of calculus to understand the paper,” says Friedman. On the other, the intro carried an implicit message, one directed towards psychologists that tacitly scolded them for accepting the theory without understanding of the math allegedly supporting it: “If you can’t understand this,” as Brown put it, “don’t allow yourself to continue reading.”

Math aside, the paper has a biting, sardonic quality. “Most of the good lines are Nick’s,” says Sokal.

In critiquing a section of Losada’s earlier research that characterized high performance teams as “buoyant” and low performance teams as “stuck in a viscous atmosphere,” to take an example, Brown wrote mockingly:

"One could describe a team’s interactions as 'sparky' and conﬁdently predict that their emotions would be subject to the same laws that govern the dielectric breakdown of air under the inﬂuence of an electric ﬁeld. Alternatively, the interactions of a team of researchers whose journal articles are characterized by 'smoke and mirrors' could be modeled using the physics of airborne particulate combustion residues, combined in some way with classical optics."

The line made it in to the final; others were struck. Friedman worked to tone down harsh language where he could, feeling protective of his profession and suspecting “how much resistance there would be,” as Barbara Fredrickson is an associate editor at the American Psychologist.

In the end, the paper that was submitted to the American Psychologist—the same journal that had peer reviewed and published Fredrickson and Losada’s theory in 2005—was relentless in its attack, tightly written and squarely focused on bad math.

And through it all, the three met only once in person, when Friedman was in London to give an academic address. It was a day spent scribbling equations in chalk on blackboards and talking strategy – a debunkers’ bonhomie.

Afterwards, Friedman and Brown downed a few beers at a local pub. None of the authors have seen each other since.

* * *

On July 2, 2012, Alan Sokal submitted the finished paper for peer review, then titled “The Complex Dynamics of an Intellectual Imposture,” to the American Psychologist.

On July 12th, they had a response. Citing the journal’s 85-percent rejection rate, Managing Editor Gary VandenBos informed Sokal that the paper had exceeded the two-month limit of which authors were allowed to respond to a target article, and was “just not right for American Psychologist at the time.”

The following day at 2:32 p.m., Sokal replied. In an appeal that “took a bit of bravado,” the team decided to go over VandenBos’ head, writing to American Psychological Association CEO Norman Anderson that this was no ordinary comment; that the paper would be published soon in some good journal; and that if it were published somewhere else it would not look good for American Psychologist. Sokal wrote that by not letting the paper go to peer review, the American Psychological Association was running the risk of converting “a minor scandal into a major one.”

Two hours later at 5:22 p.m., Anderson responded. The decision had been reversed. The paper would go under review.

When asked to comment for this article, VandenBos wrote in an email that, “the APA editorial peer review process for all of our scholarly journals is a confidential process.” But as Friedman and Sokal explain, when reviewing a paper, the managing editor first sends it to an associate editor “closest in field” to the subject addressed in the paper. The only problem with this, Sokal explains, was “that the associate editor closest in field to our paper was Barbara Fredrickson.”

“But the editor in chief, he’s honorable,” says Sokal, and so the paper was assigned to another associate editor who in turn sent it out to four reviewers.

In September, the results came in.

“The messages were mixed,” Sokal says. “One said it was ‘perfect.’ One said the content was great, but that he wanted it to be toned down. Three and four had some complaints about the tone and some rather more extensive criticisms of the content.”

They went through the paper again, removing harsh criticisms and toning down language. It was here that the title changed from “Complex Dynamics of an Intellectual Imposture” to “Complex Dynamics of Wishful Thinking.” Similarly, other references to “intellectual imposture” in the paper were removed.

As for the third and fourth reviewers’ “more extensive” criticisms, Sokal says, the team addressed “each and every” point, accepting “about 20 percent” of the commenters’ criticisms and refuting “about 80 percent” of them. The cover letter attached to the revised draft was 25-pages long. The paper was recommended for publishing.

* * *

Nearly a year later, on July 15, 2013, “The Complex Dynamics of Wishful Thinking” was published online by the American Psychologist. That same day, a response from Fredrickson was also released, called “Updated Thinking on Positivity Ratios.”

Barbara Fredrickson declined to comment for this article. In her published response she wrote that she has “come to see sufficient reason to question the particular mathematical framework,” employed in her 2005 paper.

Co-author Marcial Losada, Fredrickson wrote, “chose not to respond.” Emails sent to Losada seeking comment for this story were not answered.

While ditching the math underlying her theory—the authors issued a formal correction to their 2005 work on Sept. 16th—Fredrickson still believes that research in positivity ratios holds “logic and importance.”

“My aim in this response article is not to defend Losada’s mathematical and conceptual work,” she wrote. “Indeed, I have neither the expertise nor the insight to do so on my own. My aim, rather, is to update the empirical evidence for the value and nonlinearity of positivity ratios.”

She echoed the point in a Sept. 16th letter to the editor about “The Magic Ratio That Wasn’t,” an article written by Tom Bartlett of the Chronicle of Higher Education. Frederickson stated: “It is important to recognize that considerable theory and evidence point to the continued value of tracking and raising positivity ratios.”

“Other elements of the original article remain valid and unaffected by this change,” she wrote, “most notably the empirical finding—replicated across two independent samples—that positivity ratios were significantly higher for individuals identified as flourishing relative to those identified as nonflourishing.”

In the same letter, Fredrickson announced that future printings of her book Positivity would “feature a new note to readers” referencing the “current scientific dialogue,” and that a link to her formal correction would be included on the book’s website.

Brown, Sokal and Friedman were little satisfied with Fredrickson’s response, or the authors’ correction. Nor were they happy with the treatment they say they received at the hands of the American Psychologist.

The authors claim they agreed to let the American Psychologist show Barbara Fredrickson an advance copy of their paper to inform her response, but only if they were granted the “last word” in the form of a response to her response—an agreement they say the American Psychologist subsequently broke. (After a months-long appeals process, the authors have been granted permission to answer Fredrickson in the American Psychologist.)

Fredrickson’s response, Brown says, “totally fails to address almost any of the points we made, except to the extent that she says, ‘okay, well, if I throw my collaborator under the bus maybe that will make you happy.’”

“She claims that out of the trinity of math theory and data, we maybe lost the math, but we still have the familiar duo of theory and data you need to do science,” Brown says, “but she doesn’t because the only theoretical support she had were those equations.”

“She did the classic tar baby thing,” Friedman says. “Two out of three ain’t bad.”

There are other inconsistencies, they note, odd facts confusing Fredrickson’s claim that she studied the math but lacks the “expertise and insight” needed to defend it.

In Positivity, she states: “I needed to clear the decks to make room for this sudden new turn in my research program. I wanted to do it justice. Thanks to the John Templeton Foundation, I arranged a mini-sabbatical for the following semester. I was released from teaching duties so I could immerse myself in the science of dynamic systems that Marcial introduced me to…Having done so, I’d now like to share it with you.”

Additionally, Fredrickson references a textbook called Differential Equations, Dynamical Systems, and an Introduction to Chaos, a book Sokal says “is aimed at upper-level undergraduates in mathematics, physics and related disciplines.”

“If she had studied 1/10th of what she said she studied,” says Sokal, “she would have seen right through Losada.”

Muddying the waters still, Martin Seligman, positive psychology’s most influential figure, butchered facts relating to the critical positivity ratio in his own book, misstating that “60 companies” rather than the factual sixty business teams had been studied.

Emails sent to Seligman seeking comment on the discrepancy were not answered.

“I contacted Seligman to clarify his use of the sixty corporations research vs. sixty teams,” Friedman says, “and he responded that he wasn't sure how he came up with it. He distanced himself from the whole situation, saying that he had never endorsed the ratio as an exact number.”

The two continued dialoguing on the topic. Eventually Seligman thanked Friedman and his coauthors for helping to correct the scientific record, but “his first response was brief and seemed rather annoyed,” Friedman says. “Dismissive.”

“Very strange,” says Sokal. “It doesn’t give you confidence if two of the biggest names in the subfield are at the very least so sloppy.”

* * *

To this day, Nick Brown still smells bullshit. He smells it despite the claim that he and his coauthors make at the end of their paper that they do not, “have an opinion about the degree to which excessive enthusiasm, sincere self-deception, or other motivations may have influenced Losada and colleagues when writing their articles.”

“I don’t like people who take the piss,” he says, and that's exactly what he thought Losada did by taking his theory to Fredrickson.

In their forthcoming comment on Fredrickson’s response, they intend to detail other errors in Fredrickson and Losada’s work and argue that even the metaphor of critical positivity is groundless. “(Fredrickson's) abandoned the specific number but she's still grasping for the general concept,” Friedman says.

“It may feel like we’re taking this dead horse, flogging it, quartering it, baking it out in the sun,” Brown says. “A lot of people are saying ‘Stop already!’ And we’re going, ‘We can’t!’ When you’re dealing with people like this—particularly with people like Losada, although I must say I was disappointed by Fredrickson’s reaction too—you have to kill every point stone dead.”

In the meantime, greater questions remain, says Sokal, who notes that only one person before Brown had publicly criticized the math informing the theory—a Chilean researcher named Andres Navas who critiqued Losada’s 1999 paper in a note to the website of the French National Center for Scientific Research.

“For me, the real question is not about Fredrickson or Losada or Seligman,” Sokal says. “It’s about the whole community. Why is it that no one before Nick—and I mean Nick was a first semester part-time Master’s student, at, let’s be honest, a fairly obscure university in London who has no particular training in mathematics—why is it that no one realized this stuff was bullshit? Where were all the supposed experts?”

“Is it really true that no one saw through this,” he asks, “in an article that was cited 350 times, in a field which touts itself as being so scientific?”

In posing this question to psychologists with relevant expertise, a partial picture begins to emerge.

Some said they weren’t informed on the issue, and couldn’t comment. Others said they knew about the 2005 paper and had cited it, but with qualifications. “My opinion of the paper has always been that it was a metaphor, disguised as modeling,” said David Pincus, a psychologist at Chapman University who specializes in the application of chaos theory to psychology.

But it also emerged that others had indeed voiced direct concerns over the math underlying the theory, only to meet deaf ears.

Stephen Guastello, a psychologist specializing in nonlinear dynamics at Marquette University, wrote: “We’ve seen many sketchy metaphors in our line of work over the years. The question is how should one respond?”

In his email, Guastello included a list of errors he had found in Fredrickson and Losada’s application of the math.

“Ironically,” he wrote, “I did send American Psychologist a comment on some of the foregoing points, which they chose not to publish because ‘there wasn’t enough interest in the article.’ In retrospect, however, I see how I could have been more clearly negative and less supportive of any positive features of the original article.”

And from John Gottman, a well-known marriage researcher who has performed his own nonlinear difference equation modeling—work that Fredrickson referenced in the chapter of her book devoted to the critical positivity ratio:

“I did read the Fredrickson & Losada paper, and I wrote them because I couldn't understand their math either,” he wrote. “They never replied to my email message.”

“The essence of the criticism of the critical positivity ratio is that it takes quantitative reasoning to its absurd extreme,” he says, “that because we can talk about things in numerical terms, that that makes it scientific.”

It’s the kind of stuff that makes Nick Brown sick. Now fifty-two and "retired," he says he has plans to become an existential life coach and to continue his efforts picking apart shoddy psychological research. A few weeks ago, he finished his program in positive psychology at the University of East London. “I passed,” he says.

When asked whether or not the class was worth it, Brown responds with characteristic wit.

“A lot of people who’ve been through my experience would be wanting their money back,” he says, “but my goodness have I gotten my money’s worth.”

* * *

Vinnie Rotondaro is Narratively’s Editor at Large. He lives and writes in Brooklyn.

Kevin Huizenga works and lives in Saint Louis. He is working on Ganges #5.